The q Theory of Investment with Many Capital Goods

The "q " theory of investment, which relates investment to the ratio of market to replacement value of capital, has attracted considerable attention in a recent series of papers. For instance, a q variable has been used as an independent variable in empirical investment equations estimated by George von Furstenberg (1977), von Furstenberg et al. (1980), Burton Malkiel et al. (1979), and others. These papers, however, leave somewhat unclear the theoretical rationale for using q as an investment determinant. This has motivated work by Hiroshi Yoshikawa (1980), Lawrence Summers (1981), Michael Salinger and Summers (1981), and Fumio Hayashi (1982), who show that under certain conditions the rate of investment of a sharevalue-maximizing firm is indeed a function of q. This is an important result because it shows that investment equations with q an independent variable are not ad hoc constructions. Rather, they are grounded in a theory of the firm with an appealing behavioral hypothesis, viz, value maximization. An important assumption underlying this research is that capital can be treated as a homogeneous good. Of course, this is an extremely common assumption in the analysis of investment, and is not particularly more bothersome in the q theory context than elsewhere. Nonetheless, there are certain situations where it may be desirable or even essential to be able to study investment disaggregated by type of capital good. Thus, the purpose of this paper is to examine whether and how the q theory can be extended to this more general case.1 Intuitively, one would expect some difficulty with the q theory in the many-capitalgood context, as already noted by James Tobin and William Brainard (1977, p. 243) and by Salinger and Summers (p. 12). One way to see why is to recall the Tobin-Brainard distinction between "marginal" and "average" q. As Hayashi writes,